# Properties

 Label 2.193.abw_bkq Base Field $\F_{193}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{193}$ Dimension: $2$ L-polynomial: $1 - 48 x + 952 x^{2} - 9264 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0675123601384$, $\pm0.230069799779$ Angle rank: $2$ (numerical) Number field: 4.0.2054400.4 Galois group: $D_{4}$ Jacobians: 60

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 60 curves, and hence is principally polarizable:

• $y^2=165x^6+131x^5+171x^4+106x^3+115x^2+169x+30$
• $y^2=69x^6+78x^5+190x^4+148x^3+167x^2+152x$
• $y^2=70x^6+61x^5+11x^4+125x^3+50x^2+109x+141$
• $y^2=191x^6+38x^5+145x^4+166x^3+60x^2+169x+11$
• $y^2=154x^6+43x^5+35x^4+5x^3+131x^2+87x+144$
• $y^2=106x^6+51x^5+75x^4+58x^3+48x^2+73x+47$
• $y^2=153x^6+178x^5+80x^4+56x^3+67x^2+177x+152$
• $y^2=90x^6+73x^5+132x^4+138x^3+66x^2+116x+130$
• $y^2=158x^6+126x^5+63x^4+60x^3+139x^2+161x+145$
• $y^2=74x^6+64x^5+153x^4+187x^3+102x^2+122x+174$
• $y^2=52x^6+106x^5+137x^4+160x^3+161x^2+39x+110$
• $y^2=188x^6+46x^5+20x^4+171x^3+37x^2+139x+30$
• $y^2=47x^6+170x^5+143x^4+33x^3+133x^2+31x+44$
• $y^2=149x^6+57x^5+117x^4+42x^3+158x^2+x+38$
• $y^2=147x^6+59x^5+25x^4+80x^3+178x^2+53x+76$
• $y^2=47x^6+155x^5+99x^4+161x^3+83x^2+171x+86$
• $y^2=7x^6+127x^5+126x^4+53x^3+159x^2+21x+26$
• $y^2=64x^6+181x^5+179x^4+51x^3+180x^2+89x+102$
• $y^2=37x^6+56x^5+89x^4+74x^3+121x^2+117x+105$
• $y^2=119x^6+147x^5+12x^4+135x^3+59x^2+58x+123$
• and 40 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28890 1372679460 51673224895290 1925154747813891600 71709016301977158272250 2671085051932861814910021540 99495244227359262020013683985690 3706098379840788899452903641725337600 138048458691010890857009571047801225160090 5142167038122541242600917679806266810857166500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 36850 7187762 1387510918 267785600306 51682541600050 9974730240873362 1925122950833556478 371548729888542460946 71708904873245099619250

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.2054400.4.
All geometric endomorphisms are defined over $\F_{193}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.193.bw_bkq $2$ (not in LMFDB)